A year ago, Jon Davison, singer for Los Angeles prog-rock outfit Glass Hammer, was stunned when longtime chum and Foo Fighters drummer Taylor Hawkins called him with exciting news: Yes bassist Chris Squire told him that his band had chosen a replacement for departing vocalist Benoit David, and Davison was it.

“Taylor basically told me I was going to get the call from them. So I was just waiting and waiting,” says Davison, who watched 120 minutes tick past until Yes’ manager finally phoned.

The singer, whose airy timbre so closely resembled that of founding Yes vocalist Jon Anderson that he fronted the Yes tribute band Roundabout for two years before joining Glass Hammer, simply was invited to join — no audition necessary.

Davison — who appears with Yes on its tour stop in The City on Tuesday, performing “The Yes Album” (1971), “Close to the Edge” (1972) and “Going For the One” (1977) — stepped onstage with his idols for the first time in New Zealand, after only five rehearsals.

“There was a tour already scheduled, for Australia, New Zealand, Indonesia and Japan, seven weeks later,” he says. “Benoit had gotten sick and they had to cancel some dates, and he was ready to quit, apparently, so they wanted to go straight ahead with me.”

Two weeks after the big call, he met with Squire in Hollywood, where they began working out harmonies. Then the pair decamped to a delicatessen for lunch with Yes guitarist Steve Howe.

“It was amazing just sitting across from those guys,” Davison says. “My wife was there, too, because Yes is really great about family always being around.”

Squire also was impressed by Glass Hammer songs such as “If,” with its Roger Dean-ish cover art, and proto-prog epics such as the 11-minute “Beyond, Within” and the 24-minute coda “If The Sun.”

Davison, who has no plans to leave Glass Hammer, is also tentatively composing new material with Yes. He says he was very prepared for his first Yes show, because he had gained the band members’ trust.

But the nicest aspect has been the response from diehard Yes fans who frequented his Roundabout gigs, and who now get to watch Davison in the real McCoy.

He says, “It’s fun to see those same people at shows, because they were always so supportive. Everyone’s happy for me because this is the tribute artist’s dream come true.”